Dynamics of ligand substitution in labile cobalt complexes resolved by ultrafast T-jump

Ligand exchange of hydrated metal complexes is common in chemical and biological systems. Using the ultrafast T-jump, we examined this process, specifically the transformation of aqua cobalt (II) complexes to their fully halogenated species. The results reveal a stepwise mechanism with time scales varying from hundreds of picoseconds to nanoseconds. The dynamics are significantly faster when the structure is retained but becomes rate-limited when the octahedral-to-tetrahedral structural change bottlenecks the transformation. Evidence is presented, from bimolecular kinetics and energetics (enthalpic and entropic), for a reaction in which the ligand assists the displacement of water molecules, with the retention of the entering ligand in the activated state. The reaction time scale deviates by one to two orders of magnitude from that of ionic diffusion, suggesting the involvement of a collisional barrier between the ion and the much larger complex

Spinorial Characterizations of Surfaces into 3-dimensional pseudo-Riemannian Space Forms

We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in $\mathbb{R}^{2,1}$ to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well as for spacelike and timelike immersions of surfaces of signature (0,2), hence achieving a complete spinorial description for this class of pseudo-Riemannian immersions.Comment: 9 page

A likelihood method to cross-calibrate air-shower detectors

We present a detailed statistical treatment of the energy calibration of hybrid air-shower detectors, which combine a surface detector array and a fluorescence detector, to obtain an unbiased estimate of the calibration curve. The special features of calibration data from air showers prevent unbiased results, if a standard least-squares fit is applied to the problem. We develop a general maximum-likelihood approach, based on the detailed statistical model, to solve the problem. Our approach was developed for the Pierre Auger Observatory, but the applied principles are general and can be transferred to other air-shower experiments, even to the cross-calibration of other observables. Since our general likelihood function is expensive to compute, we derive two approximations with significantly smaller computational cost. In the recent years both have been used to calibrate data of the Pierre Auger Observatory. We demonstrate that these approximations introduce negligible bias when they are applied to simulated toy experiments, which mimic realistic experimental conditions.Comment: 10 pages, 7 figure

Spin-orbital excitation continuum and anomalous electron-phonon interaction in the Mott insulator LaTiO3_3

Raman scattering experiments on stoichiometric, Mott-insulating LaTiO$_3$ over a wide range of excitation energies reveal a broad electronic continuum which is featureless in the paramagnetic state, but develops a gap of $\sim 800$ cm$^{-1}$ upon cooling below the N\'eel temperature $T_N = 146$ K. In the antiferromagnetic state, the spectral weight below the gap is transferred to well-defined spectral features due to spin and orbital excitations. Low-energy phonons exhibit pronounced Fano anomalies indicative of strong interaction with the electron system for $T > T_N$, but become sharp and symmetric for $T < T_N$. The electronic continuum and the marked renormalization of the phonon lifetime by the onset of magnetic order are highly unusual for Mott insulators and indicate liquid-like correlations between spins and orbitals.Comment: to appear in Phys. Rev. Let

Magnon Heat Conductivity and Mean Free Paths in Two-Leg Spin Ladders: A Model-Independent Determination

The magnon thermal conductivity $\kappa_{\mathrm{mag}}$ of the spin ladders in $\rm Sr_{14}Cu_{24-x}Zn_xO_{41}$ has been investigated at low doping levels $x=0$, 0.125, 0.25, 0.5 and 0.75. The Zn-impurities generate nonmagnetic defects which define an upper limit for $l_{\mathrm{mag}}$ and therefore allow a clear-cut relation between $l_{\mathrm{mag}}$ and $\kappa_{\mathrm{mag}}$ to be established independently of any model. Over a large temperature range we observe a progressive suppression of $\kappa_{\mathrm{mag}}$ with increasing Zn-content and find in particular that with respect to pure $\rm Sr_{14}Cu_{24}O_{41}$ $\kappa_{\mathrm{mag}}$ is strongly suppressed even in the case of tiny impurity densities where $l_{\mathrm{mag}}\lesssim 374$~{\AA}. This shows unambiguously that large $l_{\mathrm{mag}}\approx 3000$~{\AA} which have been reported for $\rm Sr_{14}Cu_{24}O_{41}$ and $\rm La_{5}Ca_9Cu_{24}O_{41}$ on basis of a kinetic model are in the correct order of magnitude

Manipulation Strategies for the Rank Maximal Matching Problem

We consider manipulation strategies for the rank-maximal matching problem. In the rank-maximal matching problem we are given a bipartite graph $G = (A \cup P, E)$ such that $A$ denotes a set of applicants and $P$ a set of posts. Each applicant $a \in A$ has a preference list over the set of his neighbours in $G$, possibly involving ties. Preference lists are represented by ranks on the edges - an edge $(a,p)$ has rank $i$, denoted as $rank(a,p)=i$, if post $p$ belongs to one of $a$'s $i$-th choices. A rank-maximal matching is one in which the maximum number of applicants is matched to their rank one posts and subject to this condition, the maximum number of applicants is matched to their rank two posts, and so on. A rank-maximal matching can be computed in $O(\min(c \sqrt{n},n) m)$ time, where $n$ denotes the number of applicants, $m$ the number of edges and $c$ the maximum rank of an edge in an optimal solution. A central authority matches applicants to posts. It does so using one of the rank-maximal matchings. Since there may be more than one rank- maximal matching of $G$, we assume that the central authority chooses any one of them randomly. Let $a_1$ be a manipulative applicant, who knows the preference lists of all the other applicants and wants to falsify his preference list so that he has a chance of getting better posts than if he were truthful. In the first problem addressed in this paper the manipulative applicant $a_1$ wants to ensure that he is never matched to any post worse than the most preferred among those of rank greater than one and obtainable when he is truthful. In the second problem the manipulator wants to construct such a preference list that the worst post he can become matched to by the central authority is best possible or in other words, $a_1$ wants to minimize the maximal rank of a post he can become matched to

Efficient Estimation for Staggered Rollout Designs

Researchers are frequently interested in the causal effect of a treatment that is (quasi-)randomly rolled out to different units at different points in time. This paper studies how to efficiently estimate a variety of causal parameters in a Neymanian-randomization based framework of random treatment timing. We solve for the most efficient estimator in a class of estimators that nests two-way fixed effects models as well as several popular generalized difference-in-differences methods. The efficient estimator is not feasible in practice because it requires knowledge of the optimal weights to be placed on pre-treatment outcomes. However, the optimal weights can be estimated from the data, and in large datasets the plug-in estimator that uses the estimated weights has similar properties to the "oracle" efficient estimator. We illustrate the performance of the plug-in efficient estimator in simulations and in an application to Wood et al. (2020a,b)'s study of the staggered rollout of a procedural justice training program for police officers. We find that confidence intervals based on the plug-in efficient estimator have good coverage and can be as much as five times shorter than confidence intervals based on existing methods. As an empirical contribution of independent interest, our application provides the most precise estimates to date on the effectiveness of procedural justice training programs for police officers

When Is Parallel Trends Sensitive to Functional Form?

This paper assesses when the validity of difference-in-differences and related estimators depends on functional form. We provide a novel characterization: the parallel trends assumption holds under all strictly monotonic transformations of the outcome if and only if a stronger "parallel trends"-type condition holds for the cumulative distribution function of untreated potential outcomes. This condition is satisfied if and essentially only if the population can be partitioned into a subgroup for which treatment is effectively randomly assigned and a remaining subgroup for which the distribution of untreated potential outcomes is stable over time. We show further that it is impossible to construct any estimator that is consistent (or unbiased) for the average treatment effect on the treated (ATT) without either imposing functional form restrictions or imposing assumptions that identify the full distribution of untreated potential outcomes. Our results suggest that researchers who wish to point-identify the ATT should justify one of the following: (i) why treatment is as-if randomly assigned, (ii) why the chosen functional form is correct at the exclusion of others, or (iii) a method for inferring the entire counterfactual distribution of untreated potential outcomes

Ion confinement and transport in a toroidal plasma with externally imposed radial electric fields

Strong electric fields were imposed along the minor radius of the toroidal plasma by biasing it with electrodes maintained at kilovolt potentials. Coherent, low-frequency disturbances characteristic of various magnetohydrodynamic instabilities were absent in the high-density, well-confined regime. High, direct-current radial electric fields with magnitudes up to 135 volts per centimeter penetrated inward to at least one-half the plasma radius. When the electric field pointed radially toward, the ion transport was inward against a strong local density gradient; and the plasma density and confinement time were significantly enhanced. The radial transport along the electric field appeared to be consistent with fluctuation-induced transport. With negative electrode polarity the particle confinement was consistent with a balance of two processes: a radial infusion of ions, in those sectors of the plasma not containing electrodes, that resulted from the radially inward fields; and ion losses to the electrodes, each of the which acted as a sink and drew ions out of the plasma. A simple model of particle confinement was proposed in which the particle confinement time is proportional to the plasma volume. The scaling predicted by this model was consistent with experimental measurements

About the dynamics and thermodynamics of trapped ions

This tutorial introduces the dynamics of charged particles in a radiofrequency trap in a very general manner to point out the differences between the dynamics in a quadrupole and in a multipole trap. When dense samples are trapped, the dynamics is modified by the Coulomb repulsion between ions. To take into account this repulsion, we propose to use a method, originally developed for particles in Penning trap, that model the ion cloud as a cold fluid. This method can not reproduce the organisation of cold clouds as crystals but it allows one to scale the size of large samples with the trapping parameters and the number of ions trapped, for different linear geometries of trap.Comment: accepted for publication in the "Modern Applications of Trapped Ions" special issu